Fatigue Life and Crack Growth Prediction Using FEM Data · Fatigue Life and Crack Growth Prediction...

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Fatigue Life and Crack Growth Prediction Using FEM Data Robert A Adey, John M. W. Baynham, Sharon Mellings, Tom Curtin* Computational Mechanics BEASY, Ashurst Lodge, Southampton, Hampshire, SO40 7AA, UK Tel: +44 (0)23 8029 3223 Fax: +44 (0)23 8029 2853 Email: [email protected] *Computational Mechanics Inc, 25 Bridge Street, Billerica, MA 01821 Abstract As part of the engineering design process engineers have to assess not only how well the design satisfies the performance requirements but also how durable the product will be over its life cycle. A major cause of failure is the growth of cracks which grow due to fatigue loadings to the point where the product fails. This paper describes a new approach to predicting crack growth which combines the best features of boundary element and finite element technology. The crack and the crack growth are simulated using the boundary element model (BEASY) and the finite element model (MSC NASTRAN) are used to represent the remaining part of the structure. Examples are presented showing how this can be applied in the MSC PATRAN environment to a complex three dimensional fitting. The paper will also demonstrate how the technology can be used to provide higher resolution stress data near small details essential for fatigue calculations. Introduction The analysis of cracks within structures is an important application if the damage tolerance and durability of structures and components are to be predicted. As part of the engineering design process engineers have to assess not only how well the design satisfies the performance requirements but also how durable the product will be over its life cycle. Often cracks cannot be avoided in structures; however the fatigue life of the structure depends on the location and size of these cracks. In order to predict the fatigue life for any component, a fatigue life and crack growth study needs to be performed. The boundary element method is an ideal solution for performing crack growth analysis due to the high accuracy of the stress results computed on the surface of the structure and its ability to represent the stress field singularities near the crack front. In addition, since only the boundary of the body needs to be discretized, the complexity in meshing small details and features to obtain high fidelity data can be significantly reduced. In many cases the engineer responsible for the durability of the product only becomes involved during the later stages of the design process when analysis models have already been developed often involving substantial parts of the structure. Frequently these models have also been simplified to remove the details such as holes and fillets which play an important role in the durability of the product. Previously in order to make a fatigue or crack study for example the engineer would to have start the process of building a new model of the area of interest including the missing detail and identify the loads acting on the component or the part of the structure of interest. The new approach presented in this paper enables a user to take an existing MSC NASTRAN model and to automatically create a model suitable for fatigue and crack growth predictions without the need to be aware of the different analytical techniques used.

Transcript of Fatigue Life and Crack Growth Prediction Using FEM Data · Fatigue Life and Crack Growth Prediction...

Fatigue Life and Crack Growth Prediction Using FEM Data

Robert A Adey, John M. W. Baynham, Sharon Mellings, Tom Curtin*

Computational Mechanics BEASY, Ashurst Lodge, Southampton, Hampshire, SO40 7AA, UK

Tel: +44 (0)23 8029 3223 Fax: +44 (0)23 8029 2853 Email: [email protected]

*Computational Mechanics Inc, 25 Bridge Street, Billerica, MA 01821

Abstract As part of the engineering design process engineers have to assess not only how well the design satisfies the performance requirements but also how durable the product will be over its life cycle. A major cause of failure is the growth of cracks which grow due to fatigue loadings to the point where the product fails. This paper describes a new approach to predicting crack growth which combines the best features of boundary element and finite element technology. The crack and the crack growth are simulated using the boundary element model (BEASY) and the finite element model (MSC NASTRAN) are used to represent the remaining part of the structure. Examples are presented showing how this can be applied in the MSC PATRAN environment to a complex three dimensional fitting. The paper will also demonstrate how the technology can be used to provide higher resolution stress data near small details essential for fatigue calculations.

Introduction The analysis of cracks within structures is an important application if the damage tolerance and durability of structures and components are to be predicted. As part of the engineering design process engineers have to assess not only how well the design satisfies the performance requirements but also how durable the product will be over its life cycle. Often cracks cannot be avoided in structures; however the fatigue life of the structure depends on the location and size of these cracks. In order to predict the fatigue life for any component, a fatigue life and crack growth study needs to be performed.

The boundary element method is an ideal solution for performing crack growth analysis due to the high accuracy of the stress results computed on the surface of the structure and its ability to represent the stress field singularities near the crack front. In addition, since only the boundary of the body needs to be discretized, the complexity in meshing small details and features to obtain high fidelity data can be significantly reduced.

In many cases the engineer responsible for the durability of the product only becomes involved during the later stages of the design process when analysis models have already been developed often involving substantial parts of the structure. Frequently these models have also been simplified to remove the details such as holes and fillets which play an important role in the durability of the product. Previously in order to make a fatigue or crack study for example the engineer would to have start the process of building a new model of the area of interest including the missing detail and identify the loads acting on the component or the part of the structure of interest.

The new approach presented in this paper enables a user to take an existing MSC NASTRAN model and to automatically create a model suitable for fatigue and crack growth predictions without the need to be aware of the different analytical techniques used.

Fatigue Life Prediction Big differences in the fatigue life are frequently observed between results obtained for featured and unfeatured meshes. Engineers frequently use de-featuring to reduce the model size and to speed up the meshing process. The process is so well established that there are a number of CAD type tools which are designed specifically to defeature models. This is acceptable for applications where the overall stress levels and deformation is required but not when the aim is to determine life predictions because these are strongly influenced by such details. “The devil is in the detail”

Figure 1 Example showing the impact on model size of including detailed features in the FEM model.

In the new approach presented the user can simply build a local BEASY model incorporating all the detail necessary and the software will automatically transfer all the necessary loads and boundary conditions from the MSC Nastran finite element model. While this type of sub modeling is not entirely new, it has the benefit of providing the high fidelity stresses required for fatigue calculations as well as providing a model suitable for crack growth life prediction.

Crack growth Prediction The life of a component subject to a fatigue type of load is made up of two parts. The number of cycles until a crack initiates and the number of cycles required for the crack to grow to a size where it become unstable. The first so called life to initiation can normally be predicted based on the stress history which can be obtained from a suitable stress analysis. However the prediction of the life once the crack has initiated requires a model which can simulate the crack path and the fracture properties.

Figure 2 Predicted Fatigue Life based on an initial design mesh without features and a mesh including the features. Omitting the features results in significantly non conservative life predictions

Theoretical Background

A number of authors have studied the numerical simulation of crack growth using a variety of numerical techniques. The model presented here uses the Dual Boundary Element Method (DBEM) to predict the stress field for cracked structures and hence to predict the stress intensity factors along the crack front. The analysis method implemented is based on the theoretical foundations developed for two-dimensional analysis by Portela, Aliabadi and Rooke[2], and for three-dimensional analysis by Mi and Aliabadi[3]. In the Dual Boundary Element method, the crack in a structure is represented by special “Dual” elements that allow the stress and displacement fields to be computed on both crack faces without the need to subdivide the body along the crack boundary.

The Dual element method is a powerful solution tool for fracture mechanics, because it is a boundary only representation, the high accuracy and the methods ability to represent the high stress fields near the crack front.

Crack Modelling

The proposed approach can be clearly seen in multiple site damage calculation performed using BEASY by Cali, Citarella et al (14). The model and results can be seen in Figure 3, which shows close agreement between the experimental data and the numerical predictions. This example clearly shows the benefits of crack growth simulation as the crack path is predicted as well as the stress intensity and crack growth data. This example also shows the impact of load redistribution on the cracks as they grow and how the cracks interact with each other. This type of information cannot be obtained from analytical and textbook type crack growth solutions.

Figure 3 Simulation of multiple site damage in which the growth of four cracks is simulated. The experimental tests are shown on the left and the BEASY numerical predictions on the right.

The crack growth model not only provides data on the crack path but also the life of the structure. Figure 4 shows a comparison of the crack size versus the number of loading cycles with experimental data. This type of display can be used for design and prediction of life.

Fatigue Crack Growth Prediction

In practical applications a simple cyclic loading is not able to represent the conditions the component or structure will experience during its working life. Therefore the software has been linked to a comprehensive multi-axial loading module that enables real life loading data to be applied to the model. Another important element is the crack growth model that is used to predict the crack growth rate (da/dn). The analysis code allows a range of fatigue growth laws to be represented (for example Paris, NASGRO) and the code is linked to the NASGRO database of fatigue crack growth data for fatigue analysis. This also allows the use of retardation models for crack growth[1].

Reproduced from paper titled Multiple Site Damage (MSD) crack growth: numerical evaluations and experimental tests by C. Calì, R. Citarella, M. Perrella, Department of Mechanical Engineering, University of Salerno

N=774,000 cycles

N=1,070,000 cycles

Figure 4 Predicted crack size verses the number of loading cycles for one of the cracks shown in Figure 3. A Paris model was used for the crack growth rate.

Automatic Remeshing

In the analysis of a crack, at each iteration a series of new elements are added to the crack front. These elements are formed from the positions of the old crack front and the predicted positions of the new crack front. Where the crack intersects the surface of the component or structures the surface mesh has to be modified to represent the new geometry as the crack grows.

In some models the crack re-meshing can be very complex. Consequently when performing the meshing “manually” time constraints and model complexity can prohibit crack growth beyond a few iterations. The aim of the automatic remeshing in this software is to remove this manual work from the user to allow more detailed study of crack growth models to be performed automatically.

Figure 5 On the left is the geometric model of the fitting. On the right is the FEM model mesh

Crack Initiation

One important extension of this technique is that it is possible to use the same algorithm to add a crack into a model that has simply been defined to perform a stress analysis. This allows the generation of the model without having the task of modelling the crack. The crack can then be added anywhere on the model and a new data file automatically generated containing the crack.

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570000 620000 670000 720000 770000 820000 870000 920000 970000 1020000 1070000 1120000

N [cycles]a

[mm

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Numeric n°1

Experimental n°1

Experimental n°2

Numeric n°2

Reproduced from paper titled Multiple Site Damage (MSD) crack growth: numerical evaluations and experimental tests by C. Calì, R. Citarella, M. Perrella, Department of Mechanical Engineering, University of Salerno

BEASYBEASY

Integration with Finite Element Data As was stated earlier finite element models are developed for a number of purposes, and consequently the engineer responsible for durability may be presented with the task of rebuilding or substantially modifying an existing FEM model in order to obtain the information needed. This is particularly onerous in the case of cracks as they are in general a very small feature compared with the size of the structure or component and typically require special modelling treatment. The approach presented here overcomes many of these difficulties by combining the technologies in MSC Nastran and BEASY.

Consider the case where the engineer has a FEM model and wishes to predict if a crack will grow if it develops at a particularly highly stressed area. Depending upon the application the user has a number of choices on how the FEM data can be used to simulate the behaviour of the crack. For example

• The complete model including all the loading and restraints can be automatically transferred • A representative part of the model can be selected including the loads and restraints • In the case where there are complex non linear stresses (e.g. Residual Stress fields) the stress field can

be transformed to a part or the whole of the model

Figure 6 The sub model selected is shown. This will be automatically converted to use in the crack growth study

In some applications the original FEM model may not contain sufficient detail in the area where the crack is located (i.e. some of the geometrical details missing, poorly refined mesh etc). In this case the user can build a new geometric model of a sub section and transfer the loads and restraints.

The following examples show how the procedures work.

Example 1 In this application a fixing lug (Figure 5) is to be assessed for crack growth near one of the supporting pillars. A finite element model already exists of the overall fitting but without any crack information as the model was simply developed to obtain predictions of the general stress levels. The next few steps describe how this model can be used to obtain information about the stress intensity factors and how the crack will grow.

In this case the user has decided that the crack is sufficiently small that only a small subsection of the fitting is required to be part of the crack model. Therefore a subsection of the model is chosen in the modelling system (in this case MSC PATRAN) by selecting the finite elements to be included. (Figure 6)

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The next step is to identify the location of the crack initiation point and the size and shape of the initial crack. In this case it has been decided to initiate the crack on the corner in the area with the highest stress. (Figure 7)

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Figure 7 Predicted stress field and initiation position

The rest of the process can now be performed using the crack wizard which automatically checks the model and prompts the user for all the data required.

Figure 8 Sample screen view of the crack wizard where the user selects the size and shape of crack from the crack library

The final step is therefore to run the analysis to predict the stress intensity factors, the crack growth rate and the crack growth path.

Figure 9 View of the mesh showing how the mesh has been automatically modified to include the corner crack

Example 2 In this second example as part of an investigation into the cause of cracks found during routine maintenance a forensic simulation is performed to determine if there was a design problem or if the problem was caused during fabrication. The complete assembly consisted of a number of components bolted and welded together. The complete assembly was analysed to determine the load transfer and the general stress levels and then part of the model near the crack was automatically extracted to form a detailed model near the cracked area.

Figure 10 The local model used to predict the behaviour of cracks initiating near the bolt holes. The model, loads and boundary conditions were automatically captured from the global model.

A crack was initiated near the bolt hole to determine the fracture mechanics data so that it could be compared with the Stress Corrosion Cracking Stress Intensity Factors, as corrosion was suspected to be a factor in the failure. Figure 11 shows the predicted path of the crack as it grows from a small corner crack. At each step the SIF data is predicted along the crack front as can be seen in Figure 12.

Figure 11 The picture shows the crack front growing towards the thread in the bolt hole.

Figure 12 Predicted SIF data along the crack front. Each line represents a new front as the crack grows

Conclusions A general approach to modelling the durability of components and structures has been developed which combines BEASY and MSC NASTRAN.

The approach removes the requirement of rebuilding FEM models in order to capture the important stress raising features which significantly affect fatigue life predictions

The approach enables simple and accurate prediction of stress intensity factors and the automatic simulation of single and multiple crack growth.

The method is ideally suited for predicting data for fatigue life calculations in components and structures. Example applications have been presented demonstrating some of the capabilities of the method.

References (1) BEASY User Guide, Computational Mechanics BEASY Ltd, Ashurst, Southampton, UK, 2003.

(2) MSC.Nastran User's Manual, Version 68, The MacNeal-Schwendler Corporation, Los Angeles, CA, November 1997.

(3) Portela, A.; Aliabadi M.H; Rooke, D.P., “The Dual Boundary Element Method: Efficient Implementation for Cracked Problems”, International Journal for Numerical Methods in Engineering, Vol 32, pp 1269-1287, (1992).

(4) Mi Y; Aliabadi M.H., “Three-dimensional crack growth simulation using BEM”, Computers & Structures, Vol. 52, No. 5, pp 871-878, (1994).

(5) Neves A; Niku S.M., Baynham J.M.W., Adey, R.A., “Automatic 3D crack growth using BEASY”, Proceedings of 19th Boundary Element Method Conference, Computational Mechanics Publications, Southampton, pp 819-827, 1997.

(6) Aliabadi M.H., Rooke D.R., Numerical Fracture Mechanics, Computational Mechanics Publications, SOUTHAMPTON, U.K. 1991.

(7) Calì C., Citarella R., Perrella M., Multiple Site Damage (MSD) Crack Growth: Numerical Evaluations and Experimental Tests, Atti del Convegno Internazionale “6ICB/MF&F, 25-28 giugno 2001, Lisbona, Portogallo.

(8) “Durability Prediction Using Automatic Crack Growth Simulation”, S Mellings, J Baynham, R A Adey and T Curtin, International Committee on Aeronautical Fatigue, Toulouse, France, June 2001.